Entropy and expanding universe

If I remember right, I have on several occasions read that the second law of thermodynamics is a consequence of the very unlikely initial state of the universe, and that it is this "potential" that drives the universe.

I would rather give the credit to the fact that the universe can expand, since *any* initial state (even a "maximally relaxed" one) will become less likely, or even impossible, to re-occur as the universe expands.
In a non-expanding universe on the other hand, the probability of a maximally relaxed initial condition to re-occur would be quite likely in comparison.

As the universe expands, particles without volume will have access to an increasing number of states since they can occupy a larger number of positions in space. This, from my current point of view, would be a better explanation of the second law of thermodynamics.

We only have theory ( GR mostly) to go on, because no local effect would be large enough to be noticeable in our lives.
But GR shows that non-expanding 'bubbles' ( like the Schwarzshild space-time) can be embedded in expanding universes.

We only have theory ( GR mostly) to go on, because no local effect would be large enough to be noticeable in our lives.

Can't just the fact that entropy actually decreases be the noticeable effect of an expanding universe?
If I remember right, time-reversibility is a built-in feature of both Newton's and Einstein's equations. Can GR then really be used to disprove this proposition?

I'm getting out of my comfort level. The subject area of thermodynamics and GR is big and there a lot of papers and chapters in books. I can't find anything about expanding space and entropy though. Another problem with this hypothesis is that it doesn't seem to have any observable predictions.

Another problem with this hypothesis is that it doesn't seem to have any observable predictions.

Agreed - I can't directly come to think of any either.

Irrespective of this however, I find it to be a plausible explanation for entropy increase, and a better one than that of a highly improbable initial condition (for logical reasons that we have discussed).

Working out entropy in practice requires some kind of fine-graining process so one can count micro-states. Discrete energy states, for instance. Now, cosmic expansion may have no effect on the number of levels available, in this case, expansion would have no effect. If space-time is discretized ( as a means ) to get relative entropies, then your argument depends on whether more 'boxes" are created, or if existing boxes get bigger.

So it's possible to argue the case both ways, depending on the way the entropy is calculated.

Good thought, for sure.

Vanesch - that's an interesting link. Looks like a classical formula in a quantum context.

"...the entropy metric is defined by the
order or disorder of topological structure[.]” -J. E. Johnson

(is the following a valid observation
The entropy of the universe is a surface that has the arrow of time against its edge. Spacetime has no 3-dimensional edge, but it has a dimensional surface. Gravity (a force due to matter/energy) provides valleys in this surface (spacetime) where matter/energy clumps together and so expands away from other clumps. Large sheets and filaments (of matter/energy) collect together, and leave expanding space behind. There is both a (local) compaction and a (distant) dispersal of the matter and energy that fill space, and of space itself. The edge of the universe is its own expansion.